Restriction of a character sheaf to conjugacy classes
MetadataShow full item record
Let A be a character sheaf on a connected reductive group G over an algebraically closed field. Assuming that the characteristic is not bad we show that for certain conjugacy classes D in G, the restriction of A to D is a local system up to shift. We also give a parametrization of unipotent cuspidal character sheaves of G in terms of restriction to conjugacy classes. Without restriction on characteristic we define canonical bijections from the set of unipotent representations of the corresponding split group over a finite field to a set combinatorially defined in terms of the Weyl group.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie
Societatea de Ştiinţe Matematice din România
Lusztig, G. “Restriction of a character sheaf to conjugacy class.” Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie 106.3 (2015): 287–309.